The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
Learn more about prime numbers here:
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Answer:
k = -3.5
Step-by-step explanation:
6k ÷ 7 = -3
Multiply 7 to both sides
6k = -21
Divide both sides by 6
6k/6 = -21/6
k = -3.5
To check if the answer is correct or not, you can always plug in -3.5 for k in the equation.
6(-3.5) ÷ 7 = -3
-21 ÷ 7 = -3
-3 = -3
-3 equals -3 so it is correct that k = -3.5
2 litres every 2.5 minutes is 4 litres every 5 minutes so therefore, it is 0.8 litres/minute (800ml per minutes)
About 3.3 dollars for a taco i’d say
